A372869 Decimal expansion of the number whose continued fraction coefficients are given in A084580.

5, 8, 1, 5, 8, 0, 3, 3, 5, 8, 8, 2, 8, 3, 2, 9, 8, 5, 6, 1, 4, 5, 0, 0, 6, 0, 7, 2, 2, 8, 0, 6, 5, 5, 2, 4, 7, 7, 6, 3, 0, 5, 6, 6, 9, 6, 2, 0, 0, 9, 2, 3, 0, 1, 3, 6, 2, 1, 2, 1, 5, 5, 5, 1, 5, 7, 6, 7, 1, 0, 4, 9, 1, 2, 4, 1, 9, 5, 3, 4, 0, 8, 9, 4, 9, 2, 0, 1, 2, 6, 9, 4, 1, 4, 2, 1, 2, 9, 0, 9, 2, 8, 0, 5, 9, 2, 1, 2, 8, 8, 7, 8, 6, 1, 7, 6, 8, 0, 8, 0, 4, 1, 3, 2, 1, 3, 6, 3, 7, 5, 7, 8, 3, 2, 6

Offset

0,1

Links

Table of n, a(n) for n=0..134.

Example

0.5815803358828329856145006072280655247763056696200923013621215551576710...

Prog

(Python) # Using `sample_gauss_kuzmin_distribution` function from A084580.
from mpmath import mp, iv
def decimal_from_cf(coeffs):
    num = iv.mpf([coeffs[-1], coeffs[-1]+1])
    for coeff in coeffs[-2::-1]:
        num = coeff + 1/iv.mpf(num)
    return 1/num
def get_matching_digits(interval_a, interval_b):
    match_index = 0
    for i, j in zip(interval_a, interval_b):
        if i != j:  break
        match_index += 1
    return interval_a[:match_index]
def compute_kuzmin_digits(prec, num_coeffs):
    assert prec > num_coeffs
    mp.dps = iv.dps = prec
    coeffs = sample_gauss_kuzmin_distribution(num_coeffs)
    x = decimal_from_cf(coeffs)
    a = mp.nstr(mp.mpf(x.a), n=prec, strip_zeros=False)
    b = mp.nstr(mp.mpf(x.b), n=prec, strip_zeros=False)
    return get_matching_digits(a, b)
num = compute_kuzmin_digits(prec=200, num_coeffs=180)
A372869 = [int(d) for d in num[1:] if d != '.']

Crossrefs

Cf. A084580 (continued fraction).

Sequence in context: A275688 A330867 A193743 * A195356 A263497 A198139

Adjacent sequences: A372866 A372867 A372868 * A372870 A372871 A372872

Keyword

cons,nonn

Author

Jwalin Bhatt, Jul 04 2024

Status

approved